Properties of Bessel polynomials

The purpose of the thesis is to develop a range of properties of Bessel polynomials similar to those developed for the classical polynomials of Jacobi, Hermite and Laguere, In the first chapter the Bessel polynomials are defined and existing background theory is dealt with. Some new results concerning expansion, characterization and orthogonality are given. The second chapter is almost completely new work concerned with generating functions and recurrence relations. Similarly in chapter three a number of integrals involving Bessel polynomials are derived. Chapter four treats the question of integral transformations involving Bessel polynomials and, in particular, the transforms of Laplace, Hankel, Fourier and Riemann-Liouville are investigated in detail. The final chapter (v) looks at Bessel polynomials in two variables giving their definition and briefly discussing some of their properties.